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 A290602 Irregular triangle read by rows. T(n, k) gives the period length of the periodic sequence {A290600(n, k)^i}_{i >= A290601(n, k)} (mod A002808(n)), for n >= 1 and k = 1..A290599(n). 4
 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 2, 1, 1, 4, 2, 2, 1, 1, 2, 1, 1, 3, 3, 2, 1, 1, 6, 6, 4, 2, 1, 2, 1, 4, 1, 1, 1, 1, 1, 1, 1, 6, 1, 3, 1, 2, 1, 1, 1, 6, 1, 3, 4, 2, 1, 1, 4, 1, 4, 2, 2, 1, 4, 6, 2, 1, 3, 6, 2, 1, 3, 10, 5, 10, 10, 2, 1, 1, 5, 5, 10, 5, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The length of row n is A290599(n). See A290601 for the proof that this sequence is defined, and the definition of the type of periodicity (imin,P) with imin = A290601(n, k) and the period length P = T(n, k). LINKS EXAMPLE The irregular triangle T(n, k) begins (N(n) = A002808(n)): n   N(n) \ k  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 ... 1   4         1 2   6         2  1  1 3   8         1  1  1 4   9         1  1 5   10        4  2  1  1  4 6   12        2  2  1  1  2  1  1 7   14        3  3  2  1  1  6  6 8   15        4  2  1  2  1  4 9   16        1  1  1  1  1  1  1 10  18        6  1  3  1  2  1  1  1  6  1  3 11  20        4  2  1  1  4  1  4  2  2  1  4 12  21        6  2  1  3  6  2  1  3 13  22       10  5 10 10  2  1  1  5  5 10  5 14  24        2  2  1  1  2  1  1  1  2  2  1  1  2  2  1 15  25        1  1  1  1 ... T(5, 1) = 4 because A290600(5, 1) = 2, N(5) = A002808(5) = 10, A290601(5, 1) = 1 and {2^i}_{i>=1} (mod 10) == {repeat(2,4,8,6)} with period length 4. This is of the type (1,4). T(7, 6) = 6 because A290600(7, 6) = 10, N(7) = A002808(7) = 14, A290601(7, 6) = 1 and {10^i}_{i>=1} (mod 14) == {repeat(10, 2, 6, 4, 12, 8)} with period length 4. Type (1,6). The sequence {A290600(10, 1)^i}_{i >= A290601(10, 1)} (mod A002808(10)) = {2^i}_{i >= 1} (mod 18) is periodic with period length P = T(10, 1) = 6. Namely, {repeat(2, 4, 8, 16, 14, 10)}, of type (1,6). The periodicity types (imin,P) = (A290601(n, k), A290602(n, k)) begin: n   N(n) \ k    1     2      3      4     5     6     7     8     9      10    11 1   4         (2,1) 2   6         (1,2) (1,1)  (1,1) 3   8         (3,1) (2,1)  (3,1) 4   9         (2,1) (2,1) 5   10        (1,4) (1,2)  (1,1)  (1,1) (1,4) 6   12        (2,2) (1,2)  (1,1)  (2,1) (1,2) (1,1) (2,1) 7   14        (1,3) (1,3)  (1,2)  (1,1) (1,1) (1,6) (1,6) 8   15        (1,4) (1,2)  (1,1)  (1,2) (1,1) (1,4) 9   16        (4,1) (2,1)  (4,1)  (2,1) (4,1) (2,1) (4,1) 10  18        (1,6) (2,1)  (1,3)  (2,1) (1,2) (1,1) (1,1) (2,1) (1,6)  (2,1) (1,3) 11  20        (2,4) (1,2)  (1,1)  (2,1) (1,4) (2,1) (1,4) (2,2) (1,2)  (1,1) (2,4) 12  21        (1,6) (1,2)  (1,1)  (1,3) (1,6) (1,2) (1,1) (1,3) 13  22       (1,10) (1,5) (1,10) (1,10) (1,2) (1,1) (1,1) (1,5) (1,5) (1,10) (1,5) ... ---------------------------------------------------------------------------------- CROSSREFS Cf. A002808, A290599, A290600, A290601. Sequence in context: A342017 A062378 A073753 * A255404 A078090 A174341 Adjacent sequences:  A290599 A290600 A290601 * A290603 A290604 A290605 KEYWORD nonn,tabf AUTHOR Wolfdieter Lang, Aug 30 2017 STATUS approved

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Last modified April 14 22:47 EDT 2021. Contains 342971 sequences. (Running on oeis4.)